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26 January 2013

Castling Diversity in Chess960

After posting
First Move Diversity in Chess960,
I wondered if I could develop any sort of similar statistics for castling -- how many times did players castle to the same side, the opposite side, that sort of thing. What should have been a simple exercise turned out to be more difficult than I expected as I grappled with limitations in the database software I used.
Excuses aside, here are the results I calculated on the same 4340 games collected for the 'First Move Diversity' post. First, here are the number of players who castled in each game:-

0: 1516 (no castling)

1: 1607 (only one player castled)

2: 1217 (both players castled)

These numbers are surprising. Of the 8680 opportunities to castle, more than 50% of the time a player did not execute the option. I went back to recheck my calculations and couldn't find any errors on my part, so the reason must be elsewhere. The 'First Move Diversity' post mentioned that there were 45 games abandoned before the first move was made. I discovered that there were nearly 150 more games that had been abandoned after only a handful of moves had been made. Indeed, short games account for many of the games where no castling occurred. How many, I can't say for sure.

Of the 1607 games where only one player castled, here are the counts for castling to one side or the other:-

O-O: 883

O-O-O: 724

Of the 1217 games where both players castled, here are the relevant counts for castling:-

Both O-O: 659

Both O-O-O: 313

Both sides: 245 (both O-O & O-O-O)

It would be useful to compare these chess960 results with similar counts for traditional chess, but I didn't have time to do this. My gut feeling is that castling O-O-O occurs far more frequently in chess960 than in traditional chess.

It might also be useful to examine the castling patterns for the 56 different start positions of the King and Rooks (see
Castling Patterns Visualized
for a discussion of the basic patterns). Unfortunately, a sample of 4340 games probably isn't enough to produce valid results. I still might look at it if I find the time.